What's up with the pink sausages and onions?

Solution 1:

It may look familiar for a few reasons-

It is elsewhere in the game, such as the arcade in Hanamura:

And these characters are inspired by Taiko no Tatsujin:

Solution 2:

The "turnip-onion baby" is called Pachimari:

Where as the "pink sausage holding a leek" seems to be as yet unnamed but from the same in-game show/universe as Pachimari.

As you noticed Pachimari shows up in various locations throughout the game including movie posters in Hollywood during events, the Arcade in Hanamura, and various event and non event sprays and Player icons.

Not much is known about Pachimari thus far, though it is thought to be either a "Half-Onion Half Octopus" (Note the suckers on the green tentacles), or a "part Turnip part Octopus". It appears to be used by Blizzard as an extra flavour for part of world building. So far seems to not play any real importance in Hero Lore (with the exception of a certain Hog taking a shine to the stuffy [see below]), but it has made its way into other Blizzard games.